Compute reluctance: A magnetic material has length l = 0.07 m, cross-sectional area A = 0.014 m^2, and permeability µ = 4,500 µWb/(At·m). Find the reluctance ℜ in At/Wb.

Introduction / Context:Reluctance determines how much magnetomotive force is required to establish a given magnetic flux in a magnetic path. It mirrors electrical resistance in Ohm’s law, with the magnetic counterpart given by Hopkinson’s law: MMF = ℜ * phi.

Given Data / Assumptions:

• Length, l = 0.07 m.
• Area, A = 0.014 m^2.
• Permeability, µ = 4,500 µWb/(At·m) = 4,500 * 10^-6 Wb/(At·m) = 0.0045 Wb/(At·m).
• Uniform cross-section and material properties; linear operation (no saturation considered).

Concept / Approach:

The reluctance formula is ℜ = l / (µ * A), with units At/Wb. Substitute SI-consistent values, being careful with the micro (10^-6) prefix in permeability.

Step-by-Step Solution:

Verification / Alternative check:

Dimensional check: m / (Wb/(At·m) * m^2) = m / (Wb/At * m) = At/Wb, correct unit for reluctance.

Why Other Options Are Wrong:

11 and 111 At/Wb underestimate by factors of 100 and 10. 1 At/Wb is far too small. 7 At/Wb has no basis in the calculation.

Common Pitfalls:

Failing to convert µ from micro-units, or using µ_r instead of µ (absolute) in the formula. Always ensure SI consistency.

Final Answer:

1111 At/Wb